M1388941 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	21.3932	68.6567%	500000	15000000	0.0714	4.9025%	21.4646	70.1933%	1.5366%
PrimeNet	2⁵⁶	0.0069	62.5000%	6500	110000	0.0007	2.7579%	0.0076	63.5342%	1.0342%
GPU72	2⁶⁰	0.1106	65.0000%	5500	70000	0.0005	1.2015%	0.1111	65.4205%	0.4205%
Difference	+7	+21.2826	+3.6567%	+494500	+14930000	+0.0709	+3.7010%	+21.3536	+4.7728%	+4.7728%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

21.3932

68.6567%

500000

15000000

0.0714

4.9025%

21.4646

70.1933%

1.5366%

PrimeNet

2⁵⁶

0.0069

62.5000%

6500

110000

0.0007

2.7579%

0.0076

63.5342%

1.0342%

GPU72

2⁶⁰

0.1106

65.0000%

5500

70000

0.0005

1.2015%

0.1111

65.4205%

0.4205%

Difference

+21.2826

+3.6567%

+494500

+14930000

+0.0709

+3.7010%

+21.3536

+4.7728%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1388941	612227525470481	15	49.121	220393640 2³ × 5 × 109 × 50549	-	109	50549	6.755e-5	0.0002	0.0003
1388941	55925765815509465872137	23	75.566	20132520321420948 2² × 3 × 7² × 35897 × 953811743	2018-08-10	35897	953811743	10,718	2.8788	5.3733

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1388941

612227525470481

49.121

220393640
2³ × 5 × 109 × 50549

109

50549

6.755e-5

0.0002

0.0003

1388941

55925765815509465872137

75.566

20132520321420948
2² × 3 × 7² × 35897 × 953811743

2018-08-10

35897

953811743

10,718

2.8788

5.3733

exponent	prime factors	composite factor	digits	bits*
1388941	612227525470481 55925765815509465872137	34239293215270977131617110983913887897	38	124.687

exponent

prime factors

composite factor

digits

bits*

1388941

612227525470481
55925765815509465872137

34239293215270977131617110983913887897

124.687

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
unknown			500000	15000000		-	skipped known factor: 612227525470481	-	-	0.071	-	-	4.903%

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.330 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.330 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	11.70
50000	5000000	55925765815509465872137	2	0.094
250000	35000000		50	13.54

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-15T08:59:47	Oliver Kruse	ECM-HTC	50000	5000000						3	0.141
2018-08-10T00:05:08	Chang Chia-Tche	exbpc13	50000	5000000	55925765815509465872137	75.566	2	2		2	0.094
2018-12-21T12:14:11	TJAOI	Manual testing	50000	5000000						246	11.56
2021-09-17T08:20:44	TJAOI	Manual testing	250000	35000000						50	13.54

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T13:37:42

Oliver Kruse

GTX-2

612227525470481

AE50AEAB527862__

2017-10-25T09:33:12

Chang Chia-Tche

homura

612227525470481

AE50AEAB527862__

2018-08-10T00:15:44

ATH

ec2-PRPCF

612227525470481

55925765815509465872137

19C6BA7368D98D__

2018-08-11T06:29:21

arnaud

stm-11-010

612227525470481

55925765815509465872137

19C6BA7368D98D__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront